Puzzle time - prime test

[jon-nyc]

Does 4^9 + 6^10 + 3^20 happen to be a prime number?

[jon-nyc]

I cheated and calculated the sum and checked it against known primes so I have the answer. But I’m sure there’s a clever answer.

[jon-nyc]

I have the clever solution. They could have made this problem with larger numbers so the brute force method was not possible.

[Klaus]

:::

(a-b)^2 = a^2-2ab+b^2.

It's a square number. End of story.

:::

[jon-nyc]

Yep, and to my point that they could have made it not solvable through brute force, it works for any 3^n and 2^(n-1).

So ask about 4^999 + 6^1000 + 3^2000

[jon-nyc]

2 weeks in a row they gave easy problems. Kinda disappointing.

[Klaus]

But, to be honest, it was easier to derive the "clever" solution from the "brute force" solution than arriving directly at the "clever" soluton.